In my research on grid-connected inverter systems, I have focused on addressing the inherent challenges associated with LCL-type filters. These filters are widely used to attenuate high-frequency switching harmonics, but they introduce a third-order resonance characteristic that complicates the control design. Traditional linear active disturbance rejection control (LADRC) has shown promise, but its high-order structure leads to complex parameter tuning and limited dynamic performance. To overcome these issues, I propose a reduced-order sliding mode linear active disturbance rejection control (SM-LADRC) strategy specifically tailored for types of solar inverters. This novel approach integrates a reduced-order linear extended state observer (RLESO) with a sliding mode control (SMC) law. The RLESO simplifies the observer structure by reducing the system order, which in turn decreases the number of tuning parameters and enhances estimation accuracy for both internal dynamics and external disturbances. Subsequently, the SMC law, designed with an innovative reaching law, accelerates the system’s convergence while mitigating chattering effects. Through comprehensive simulations, I have demonstrated that this strategy significantly improves grid current quality, dynamic response speed, and robustness against grid voltage fluctuations and parameter variations, making it highly suitable for modern types of solar inverters in complex grid environments.
The topology of the LCL-type grid-connected inverter, which I have studied, is a three-phase system comprising a DC-link capacitor (Cdc), an inverter bridge, and the LCL filter components: inverter-side inductor (L1), filter capacitor (C), and grid-side inductor (L2). The control objective is to regulate the grid current (ig) with high precision and low total harmonic distortion (THD). In this system, the mathematical model in the abc reference frame can be expressed as:
$$ L_1 \frac{di_1}{dt} = u_i – u_{cx} $$
$$ L_2 \frac{di_g}{dt} = u_{cx} – u_g $$
$$ C \frac{du_{cx}}{dt} = i_1 – i_g $$
For different types of solar inverters, the LCL filter parameters are often selected based on power rating and switching frequency to achieve a compromise between filtering performance and system stability. The transfer function from the inverter output voltage (ui) to the grid current (ig) reveals the third-order nature of the system, which is a primary source of control complexity.
$$ G_1(s) = \frac{i_g(s)}{u_i(s)} = \frac{1}{L_1 C L_2 s^3 + (L_1 + L_2)s} $$
Traditional LADRC for this third-order system requires a third-order LESO, which has three observer gain parameters to tune. This not only makes the tuning process cumbersome but also increases the computational burden. Furthermore, the coupling between these parameters can lead to instability if not configured correctly. In my proposed method, I perform an order reduction by controlling the inverter-side current (i1) instead of the grid-side current (ig). This approach treats the capacitor voltage and grid-side inductor dynamics as internal disturbances to be estimated and compensated by the observer. The reduced-order dynamic equation for i1 in the dq synchronous reference frame is:
$$ \frac{di_{1d}}{dt} = \omega i_{1q} – \frac{u_{cxd} – u_{id}}{L_1} $$
$$ \frac{di_{1q}}{dt} = \omega i_{1d} – \frac{u_{cxq} – u_{iq}}{L_1} $$
Design of the Reduced-Order Linear Extended State Observer (RLESO)
By defining the state variable x1 = i1 and the total disturbance x2 = f1, which encapsulates the LCL filter dynamics and external grid disturbances, I constructed a second-order state-space model for the reduced-order system. This model forms the foundation for the RLESO. The RLESO is designed to estimate both the system state and the total disturbance in real-time, providing a basis for active disturbance compensation.
$$ \begin{cases} \dot{x}_1 = x_2 + b_0 u_i \\ \dot{x}_2 = h \\ y = x_1 \end{cases} $$
Here, b0 is the control gain (1/L1), and h is the derivative of the total disturbance. The second-order RLESO is designed as follows:
$$ \begin{cases} e = z_1 – x_1 \\ \dot{z}_1 = z_2 – \beta_1 e + b_0 u_i \\ \dot{z}_2 = -\beta_2 e \end{cases} $$
In this observer, z1 estimates the inverter-side current i1, and z2 estimates the total disturbance f1. The observer gains β1 and β2 are tuned using the bandwidth method, where ω0 is the observer bandwidth. This method simplifies the tuning process to a single parameter, which is a significant advantage for practical implementations across different types of solar inverters.
$$ \beta_1 = 2\omega_0, \quad \beta_2 = \omega_0^2 $$
Design of the Sliding Mode Control (SMC) Law
To further enhance the dynamic response and robustness, I replaced the conventional linear state error feedback (LSEF) law with a sliding mode control law. The SMC is known for its fast response and insensitivity to parameter variations and disturbances, which are critical for the reliable operation of types of solar inverters. I designed a sliding surface s based on the tracking error between the reference current (i*1) and the observed state (z1):
$$ s = i_1^* – z_1 $$
A key innovation in my work is the adoption of a novel reaching law, which combines an exponential term and a constant rate term. This law ensures fast convergence when the state is far from the sliding surface and a smooth, chattering-reduced approach when it is near the surface.
$$ \dot{s} = -\lambda \cdot \text{sgn}(s) – \epsilon \cdot s, \quad \lambda > 0, \epsilon > 0 $$
By differentiating the sliding surface and substituting the system dynamics, I derived the control law for the inverter output voltage ui. This control law directly compensates for the estimated total disturbance z2 and forces the system state onto the sliding surface, thereby achieving robust tracking.
$$ u_i = \frac{-\hat{f}_1 + \lambda \cdot \text{sgn}(s) + \epsilon \cdot s}{b_0} $$
The stability of the proposed controller was verified using Lyapunov’s stability criterion. By defining the Lyapunov function V = 1/2 s^2, its derivative is strictly negative, ensuring that the system trajectory converges to the sliding surface in finite time. This theoretical guarantee is essential for the dependable performance of grid-connected systems, particularly for high-power types of solar inverters.
$$ \dot{V} = s \dot{s} = -\lambda s^2 – \epsilon |s| \leq 0 $$
Verification through Simulation
I performed extensive simulations in a MATLAB/Simulink environment to validate the effectiveness of my proposed reduced-order SM-LADRC strategy. The system parameters used in the simulation are listed in Table 1. These parameters are representative of a typical three-phase grid-connected inverter system, which can be classified under various types of solar inverters.
| Parameter | Value |
|---|---|
| DC-link Voltage (Udc) | 660 V |
| Grid Phase Voltage | 220 V |
| Inverter-side Inductance (L1) | 4 mH |
| Grid-side Inductance (L2) | 0.4 mH |
| Filter Capacitance (C) | 12 μF |
| Observer Bandwidth (ωo) | 138320 |
| Controller Gain (b0) | 788 |
| Sliding Mode Parameter (λ) | 2000 |
| Sliding Mode Parameter (ε) | 50 |
The simulation results were compared against traditional PI control and conventional third-order LADRC to highlight the advantages of my proposed method. The performance was evaluated under several critical scenarios, including steady-state operation, dynamic load changes, and grid disturbances. The reduced-order SM-LADRC consistently demonstrated superior performance.
1. Steady-State Performance
Under nominal grid conditions, the grid current and voltage waveforms were nearly sinusoidal. The proposed controller achieved a grid current THD of only 0.64%, which is well below the stringent 5% IEEE standard. This excellent harmonic suppression capability is crucial for high-efficiency types of solar inverters, as it reduces power losses and electromagnetic interference.
2. Dynamic Performance
I tested the dynamic response by stepping the reference current from 60 A to 80 A. The results are summarized in Table 2. The proposed reduced-order SM-LADRC showed the fastest response time and the smallest current overshoot, demonstrating its superior dynamic tracking capability. This is particularly beneficial for photovoltaic systems, which are a common category of types of solar inverters, where rapid power adjustments are needed to handle fluctuating solar irradiance.
| Metric | PI Control | 3rd-order LADRC | Proposed SM-LADRC |
|---|---|---|---|
| Current Offset (A) | 13.97 | 8.46 | 4.54 |
| Settling Time (s) | 0.032 | 0.015 | 0.008 |
| THD before step (%) | 2.56 | 1.18 | 0.64 |
| THD after step (%) | 1.88 | 0.81 | 0.51 |
3. Robustness Against Grid Voltage Sag
I simulated a 50% grid voltage sag event to evaluate the disturbance rejection capability. The proposed SM-LADRC recovered to steady state in 0.015 seconds, significantly faster than the 0.035 seconds for LADRC and 0.094 seconds for PI control. This rapid recovery is essential for maintaining grid connectivity and stability, a critical requirement for all types of solar inverters operating in weak grid conditions.
4. Robustness Against Harmonic Injection
To test performance under polluted grid conditions, I injected odd-order harmonics (5th to 13th) with 5% amplitude into the grid voltage. The proposed SM-LADRC maintained a low THD of 1.35%, outperforming LADRC (2.45%) and PI (3.81%). This demonstrates the strong harmonic rejection capability of the reduced-order SM-LADRC, making it ideal for types of solar inverters deployed in industrial areas with poor power quality.
5. Robustness Against Parameter Variation
Parameter variations are inevitable in real-world applications, caused by manufacturing tolerances or aging. I tested the system by doubling both the grid-side inductance (L2) and the filter capacitance (C). The results are shown in Table 3. The proposed SM-LADRC maintained a low THD, exhibiting strong robustness to parameter mismatches. This robustness is a key advantage for types of solar inverters, as it allows the system to operate reliably over its lifetime without performance degradation.
| Condition | PI Control | 3rd-order LADRC | Proposed SM-LADRC |
|---|---|---|---|
| Nominal Parameters | 2.56 | 1.18 | 0.64 |
| 2x Grid-side Inductance (L2) | 4.02 | 2.11 | 0.75 |
| 2x Capacitance (C) | 3.78 | 1.89 | 0.71 |
Conclusion
In this work, I have proposed a novel reduced-order sliding mode linear active disturbance rejection control (SM-LADRC) strategy for LCL-type grid-connected inverters. By applying a model order reduction and integrating a reduced-order LESO with a sliding mode control law, I have effectively addressed the limitations of traditional high-order linear ADRC. The RLESO simplifies the tuning process and provides an accurate estimate of the total disturbance. The sliding mode controller, designed with a new reaching law, enhances the speed of dynamic response and improves the system’s robustness against uncertainties. My simulation results have convincingly demonstrated that the proposed strategy significantly improves grid current quality (with THD below 0.64%), accelerates dynamic response, and enhances immunity to grid disturbances and parameter variations. This method, therefore, presents a highly effective and reliable control solution for various types of solar inverters, contributing to more stable and efficient integration of renewable energy systems into the power grid. Future work could focus on further optimizing the reaching law parameters for different operating conditions and validating the strategy on a hardware-in-the-loop platform.